You can use all-purpose flour to make pasta, but for this eggless version, I think you need the strength of semolina flour. I would be worried that an AP flour pasta made without eggs might be too delicate or get gummy. Of course, there's nothing wrong with experimenting!

If you work fast enough, you don't need the towel dampened. I try to avoid it because I don't want my pasta getting wet and mushy, but if you're making a lot, a very lightly dampened towel is a good idea.